Planning Christmas trip and have to have negative Covid test 5 days before travel. Let's say one of us is positive but asymptomatic. Obviously we would quarantine but how long would we continue to test positive - we've heard you could still test positive a few weeks after, even if never exhibit symptoms.

My dad tested positive a month after he was over covid. Some of those tests will say positive long after you are contagious or symptomatic.

If you can prove that you've had multiple positive tests dating back longer then 10 days, some US places may let you still travel since the CDC says you have 90 days to continue to test positive if you're currently not symptomatic.

If you're trying to go out of country, they can pretty much tell you to pound sand. I wouldn't expect anything but a negative test to get clearance.

Nick Saban needed 3 consecutive negatives over 3 days to be released back onto the field.

We have had patients test positive for 28 days after onset of very mild symptoms so for those who test positive from an employee perspective we allow them to return no less than 10 days after onset of symptoms as long as they are symptom free for the 24 hours before returning to work.

I would think for travel sake the above would apply as well.

Who is requiring you to have a negative test before traveling?

Gizzards said:

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Who is requiring you to have a negative test before traveling?

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USVI - have to have negative test 5 days before travel - results must be logged in to their travel portal and bring proof with you. Mixed comments on how strict they are when you land in STT.

So we are crossing fingers no one in the family unknowingly shows up positive.

This doesn't EXACTLY answer your question, but I think the study gives a lot of helpful information about the duration of shedding of nonviable virus (and positive test results) with COVID.
https://www.thelancet.com/journals/lanmic/article/PIIS2666-5247(20)30172-5/fulltext
For the TL;dr crowd, viable particles are shed for only 9 days from the upper respiratory tract (and hence contagious potential), while inactive virus particles can be shed for up to 83 days after infection.
MY answer to your question would be 9 days from the onset of symptoms with a confirmatory positive test OR 9 days after a positive test in an asymptomatic patient.
As is stated in responses above, places of work and those regulating travel are still stuck in thinking a negative test is necessary to prove a person is no longer contagious.